The primitive cohomology of theta divisors

Abstract

The primitive cohomology of the theta divisor of a principally polarized abelian variety of dimension $g$ is a Hodge structure of level $g-3$. The Hodge conjecture predicts that it is contained in the image, under the Abel-Jacobi map, of the cohomology of a family of curves in the theta divisor. We survey some of the results known about this primitive cohomology, prove a few general facts and mention some interesting open problems.

To appear in the proceedings of the conference on Hodge Theory and Classical Algebraic Geometry at the Ohio State University, May 2013

References in corpus (1)

• Hurwitz spaces of Galois coverings of P^1 with Galois groups Weyl groups